fan impeller
Dorde S. ˇCantrak
1,a, Vesna Mila Z. ˇColi´ c Damjanovi´ c
2and Novica Z. Jankovi´ c
11 University of Belgrade, Faculty of Mechanical Engineering, Belgrade, Serbia
2 University of Belgrade, Faculty of Architecture, Belgrade, Serbia
Received 27 May 2015, Accepted 29 February 2016
Abstract – Experimental research of the turbulent swirl flow in the pipe behind the axial fan impeller is presented in this paper. Axial fan is inbuilt without guide vanes in the installation with a free inlet and ducted outlet, like it is widely used in the ventilation systems. One-component laser Doppler anemometry and stereo particle image velocimetry (SPIV) are used in two measuring sections on the fan pressure side and for three fan rotation numbers. Non-dimensional axial velocity profile is not significantly transformed downstream, while the circumferential is, although it preserves its character. Turbulence level is the highest in the vortex core in both measuring sections for all velocities. It increases downstream in the vortex core zone and decreases in the main flow region. Determined skewness and flatness factors point out the intermittent character of the generated turbulent swirl flow, as well as the existence of the organized coherent structure. Correlation curves indicate various dynamics of fluctuating circumferential velocity fields in measuring points. The Rankine vortex structure of the turbulent swirl flow is also revealed by the SPIV measurements. Analysis shows more dominant vortex core dynamics in the downstream section.
Studied flow is characterized by extensive mass, momentum and energy transfer.
Key words: Axial fan / turbulent swirl flow / PIV / LDA
1 Introduction
Turbulent swirl flow occurs in numerous techni- cal systems, as well as in nature. They are present in turbomachinery, cyclones, combustion processes, magneto-hydrodynamic generators, inducers etc. A vor- tex structure at the inlet of an inducer is studied in ref- erence [1], while mean and turbulent features of inducer inlet flow for various centrifugal pump duty points are an- alyzed in reference [2]. Paper’s focus is on the turbulent swirl flow generated by the axial fan in a straight pipe, where it can be studied as the swirl flow generator, i.e., inducer. Ducting adjacent to an axial fan have a consid- erable effect on the fan duty point. It is shown that a fan will achieve its optimum performance when the flow at the inlet is fully developed with symmetrical air ve- locity profile which is free from swirl. Similar situation is necessary at the fan discharge [3]. It is also reported in reference [3], page 102: “In the case of tube axial fans, the problem can be especially severe with swirl existing up to almost 100 diameters of ducting. The only solution is to incorporate a flow straightener, which destroys the swirl,
a Corresponding author:djcantrak@mas.bg.ac.rs
or guide vanes which can recover the swirl energy”. This is also shown in reference [4].
This paper presents a study of the turbulent swirl flow on the axial fan pressure side by the use of the laser- based, measuring techniques such as particle image ve- locimetry (PIV) and laser Doppler anemometry (LDA) in the ventilation ducts.
The paper’s focus is on the turbulent swirl flow gen- erated by the axial fan in a straight pipe. It is inbuilt without guide vanes in the installation with a free in- let and ducted outlet categorized as B installation type in ISO 5801. It is widely used in ventilation systems in this way. This case is studied theoretically, experimentally and numerically, not exclusively, but thoroughly in refer- ences [4–10]. Installation of the C category after ISO 5801 has been recently studied in reference [11]. The develop- ment of the mean velocity field of the turbulent swirl flow in straight pipes is described with a thorough overview in reference [12]. Complex analysis of turbulent swirl flow, which is of interest in HVAC systems, is given in refer- ence [13]. Some aspects of application of the laser-based measurement and visualization techniques in ventilation systems are reported, not only in reference [6].
W
w Fluctuating circumferential velocity, m.s−1 x, y Target coordinate system, mm
z Axial coordinate along a pipe axis, m Greek symbols
α Dimensionless radius
βR Blade angle at impeller diameter,◦ Γ Average circulation, m2.s−1 ν Kinematic viscosity, m2.s−1
σ Root-mean-square of the turbulent velocity fluctuations, m.s−1
τ Correlation time, s
ϕ Coordinate of the polar cylindrical coordinate system,◦
Ω Swirl flow parameter
Experimentally obtained and presented results in this paper show the turbulent swirl flow durability. Namely, the turbulent swirl flow with the Rankine vortex struc- ture, generated by the specially designed axial fan, sur- vived till the downstream measuring section, which is almost at the test rig outlet. Velocity profile has been changed, but not significantly. Experimentally deter- mined skewness and flatness factors reveal the intermit- tent character of the generated turbulent swirl flow and existence of the organized coherent structure. In addition, the calculated correlation curves indicate various dynam- ics of the fluctuating circumferential velocity fields in var- ious flow regions.
Vortex core dynamics is documented in this paper by the PIV study and analysis. It is shown that the vortex core dynamics is greater in the downstream measuring section. This is of great importance for the ventilation systems design.
2 Experimental test rig
Experimental test rig is presented in Figure 1. The first measuring section is positioned inz/D= 3.35, while the second inz/D= 26.31, wherezis the axial coordinate measured from the test rig inlet, i.e., the plane tangential
to generate the Rankine vortex, i.e., the circumferential velocity distribution rW = const., where r is a radius andW is time averaged circumferential velocity. Fan in- built characteristics are defined in Figure2b. Inlet cap is a part of the fan hub (Fig. 2b pos. 1) and has equation y= (ax2+bx+c)/(x3+dx2+ex+f), wherexis axis along the pipe axis, a, b, c, d, e and f are constants. Profiled cap at the fan discharge side (pos. 2 at Fig. 2b) is de- fined with two radii: R52 with center at the pipe axis and 108 mm from the cap bottom and R200 with the center on the cap basis diameter.
The fan rotation speed was regulated by a fully au- tomated thyristor bridge with an error up to ±0.5 rpm.
Measurements were performed on the characteristic ax- ial fan impeller rotation number n = 1000, 1500 and 2000 rpm, which generated the extensively turbulent swirl flow.
3 Measurement techniques
The study of the turbulent swirl flow employed laser-based measuring techniques, such as laser Doppler anemometry (LDA) and stereo particle image velocime- try (SPIV). Stereo PIV and LDA measurements were per- formed on the axial fan pressure side in the specified mea- suring sections (positions 4 and 5 in Fig.1).
3.1 Laser Doppler anemometry (LDA)
The LDA measurements were performed subsequently for all three velocity components using a one-component LDA system along the vertical diameter at the points, at a 10-mm distance each, in specified sections (Fig.3). A half plane above the pipe axis is denoted asφ= 90◦, while un- der the pipe the axis isφ= 270◦(Fig.5a). The laser was mounted on the computer controlled linear guides. The system works in a backscattered mode. The LDA system is a Flow Explorer Mini LDA, Dantec, with signal proces- sors BSA F30. Light wavelength is 660 nm and the optics used had a focus 300 mm. Measuring uncertainty of the used LDA system, after manufacturer’s specification, is 0.1% for the whole system. In addition, a brief overview
Fig. 1.Experimental test rig: 1 – DC motor, 2 – axial fan impeller, 3 – profiled free bell–mouth inlet, 4 – first measuring section for LDA and stereo PIV measurements (z/D= 3.35) and 5 – second measuring section for LDA and stereo PIV measurements (z/D= 26.31).
(a) (b)
Fig. 2.Axial fan impeller: (a) dimensions in the meridian plane and (b) inbuilt dimensions.
of uncertainty sources in the LDA measurements is re- ported in reference [14]. Estimation of LDA measuring volume positioning in a cylindrical pipe due to optical aberrations caused by the pipe wall curvature is studied in references [14,15]. The transit time was used as the weighting factor. Recording time of 10 s was set up as a stop criterion for all measurements. Data frequency varied along the vertical diameter, depending of the measured velocity component. Data validation during the test was, on average, 85%. Sensitivity was adjusted to the values 1200–1400 V. The acquisition and part of data process- ing were done in the BSA software, while the major part of data processing was done by the self-made programs.
The flow was seeded by an Antari Z3000II fog machine with liquid “Heavy fog”. It was naturally sucked in the test rig by the fan and consequently enough seeding was obtained.
3.2 Stereo particle image velocimetry (SPIV)
Figure 3b displays the stereo PIV calibration in the first measuring cross-section, i.e., z/D = 3.35. Stereo PIV measurements were performed in the cross-section
and vertical meridian section with origins in specified measuring sections.
The target coordinate systems, defined as in the In- sight 3G software, are presented in Figure 4, which cor- responds to Figure3a.
The laser and cameras form a back scat- ter Scheimpflug setup. Dual head Nd:YAG laser (30 mJ/pulse, wavelength 532 nm, and 15 Hz) illu- minated the flow. Two 12-bit CCD cameras with the resolution of 1660×1200 pixels and 32 fps were used.
Data acquisition and raw images data processing were performed by the Insight 3G software, while post- processed in Tecplot. Two data sampling modes were used, first with 2 Hz, when 400 pictures were collected, and the second one with 7 Hz, when only 99 raw images were collected. Raw images processing was performed using the CDIC (central difference image correction) deformation algorithm in combination with FFT corre- lator [16]. This is a four-pass method and it employed a square interrogation area of 32 px. Velocity vectors were validated using the velocity range criteria and 3×3 local median filter, while missing vectors were interpolated using a 3×3 local mean technique. The same seeding was used as in the LDA measurements.
(a) (b)
Fig. 3. Measurements in sectionz/D = 3.35: (a) One-component LDA measurements: circumferential velocity in measuring section: 1 – LDA laser, 2 – linear guide, 3 – profile inlet, 4 – axial fan and 5 – seeding; (b) Stereo PIV system calibration in the first cross-section: 1 – left and 2 – right CCD camera, 3 – Nd:Yag laser, 4 – target and 5 – linear guide.
(a) (b)
Fig. 4.Target coordinate systems definition for measurements in: (a) cross-section (view from the fan side): 1 – Nd:YAG laser and 2 – cameras and (b) vertical meridian section (view from above): 1 – left and 2 – right camera.
4 Experimental results and analysis
4.1 LDA measurements 4.1.1 Integral characteristics
Experimentally obtained distributions of time aver- aged axial and circumferential velocity fields for all three regimes, generated by the axial fan impeller, in the mea- suring sectionz/D= 3.35 are presented in Figure5.
It is obvious that the generated circumferential veloc- ity profile (W) is similar to the model of the solid body- potential swirl, i.e., the Rankine vortex. In the central zone, the turbulent vortex core is formed, known as the forced vortex region, with the solid body distribution of circumferential velocity, whereW ∝r. This domain, with
a shear layer characterized byW ≈Wmax, is connected to the sound (or main) flow region or free vortex, whereU ≈ const, and circumferential velocity has the distribution of the potential swirlW ∝1/r. The fourth – the wall region is characterized by the properties of flow in a boundary layer, which is not quantified in these experiments. A re- verse flow exists in both measurement sections (Fig.5a).
It is obvious that the character of the curves is similar for all three regimes in all four flow regions.
On the basis of experimentally obtained distribu- tions of time averaged axial (U) and circumferential (W) (Fig. 5) velocities obtained by the one-component LDA in the measuring section z/D = 3.35, the flow inte- gral characteristics were calculated: the volume flow rate (Q), the average velocity in volume (Um = Q/(R2π)),
(a) (b)
Fig. 5. Radial distribution of time averaged velocities in measuring sectionz/D = 3.35 for all three regimesn = 1000, 1500 and 2000 rpm: (a) axial velocity (U) and (b) circumferential velocity (W).
Table 1.Calculated integral parameters in the measuring section z/D= 3.35.
Regime [rpm] Integral parameters
Q[m3.s−1] Um[m.s−1] Re Γ [m2.s−1] Ω
1000 0.86 6.68 182602 5.41 0.79
1500 1.305 10.13 277018 7.91 0.81
2000 1.741 13.52 369612 10.51 0.82
the Reynolds number (Re = UmD/ν, where ν is kinematic viscosity), the average circulation (Γ = 4π2R31
0 U W(r/R)2d (r/R)/Q) and the swirl number (Ω = Q/(RΓ), where R is the inner pipe radius in this cross-section). Calculated integral parameters for the measuring section z/D= 3.35 are given in Table1.
Averaged velocity fields evolution is shown with radial-axial distributions in Figure6 for one regimen= 1500 rpm. Circumferential velocity strongly influences the distributions of axial (U) and radial (V) velocities. It is obvious that the downstream transformation of the circumferential velocity is more intensive than the axial velocity (Fig. 6). Circumferential velocity W decreases downstream in all points of the cross-section, but pre- serves the character of the Rankine vortex (Fig. 6b).
The reverse flow region is preserved for the regime n= 1500 rpm, also in the downstream region.
Calculated integral parameters for the sectionz/D= 26.31 and regime n = 1500 rpm are: Q = 1.27 m3.s−1, Um = 10.11 m.s−1, Re = 275 344, Γ = 5.4 m2.s−1 and Ω = 1.17. Relative difference in the measuring sections z/D= 3.35 andz/D= 26.31 between the obtained vol- ume flow rates for the same regime, defined by the ax- ial impeller rotation number n = 1500 rpm, is 2.68%.
It is shown that the swirl flow decays downstream, as expected.
Downstream transformation of the radial velocity for the same regime (n= 1500 rpm) is shown in Figure 6c.
It has higher values in the main flow region in the section z/D = 3.35 than in the section z/D= 26.31, while the opposite situation is in the vortex core region.
4.1.2 Turbulence statistics
Figure 7 shows the turbulence levels for all three regimes for circumferential velocity (σw/Um) in the mea- suring section z/D= 3.35. Here, the study involved the influence of the fan rotation number on the statistical characteristics of the generated field of the circumferential fluctuating velocities due to the dominant role of the cir- cumferential velocity. Studied parameters of this influence are the turbulence level, skewness and flatness factors.
Turbulence intensities in axial (σu), radial (σv) and circumferential (σw) directions are defined after the fol- lowing expressions:
σu=
u2 1/2
=
⎡
⎣1 T
T 0
u2dt
⎤
⎦
1/2
, σv =
v2 1/2
, σw=
w2
1/2
, (1)
(a) (b)
(c)
Fig. 6. Radial distribution of time averaged velocities in measuring sections z/D = 3/35 and z/D = 26.31: (a) axial (U), (b) circumferential (W) and (c) radial (V) velocity.
whereui=u, v, ware axial, radial and circumferential ve- locity fluctuations. The values of the normalized central moments for all three velocity components of the thirdSi
(skewness), and the fourth orderFi (flatness) are calcu- lated as follows:
Si=u3i/σ3i,Fi=u4i/σi3. (2) For normal, i.e., Gaussian statistical distributions, the skewness factor has the value 0, while the flatness fac- tor equals 3 (Si = 0 andFi = 3).
The highest sampling rates are achieved for circum- ferential velocity. The character of the turbulence level (σw/Um) distributions is similar for all regimes. The high- est turbulence levels, for all regimes, are achieved in the region up to r/R = 0.2. Namely, (σw/Um)max ≈0.28 is
achieved for the highest rotation number n= 2000 rpm (Fig.7a). In this region the highest turbulence level gradi- ents are also achieved. More uniform distributions occur in the sound flow region. The sign of the skewness fac- tor for circumferential velocity (Sw) determines the di- rections of the turbulent diffusion.Swis not equal to zero and changes its sign for all three regimes.
Figure8shows the downstream evolutions of distribu- tions of the turbulence level (σw/Um) as well as normal- ized correlation moments of the third and fourth order for fluctuating velocities in the circumferential directionSw
and Fw for the regimen = 1500 rpm. The circumferen- tial velocity downstream transformation, its influence on the other two components, and the highest sampling rates (in some cases higher than 30 kHz) were the main reasons
(a) (b)
Fig. 7. Influence of the fan rotation number (n) on statistical parameters for the circumferential velocity in the measuring sectionz/D= 3.35: (a) turbulence level (σw/Um) and (b) skewness factor (Sw).
(a) (b)
Fig. 8.Downstream evolution of the statistical moments of the circumferential velocity for regimen= 1500 rpm: (a) turbulence level and (b) skewness and flatness factors.
for its presentation. It is obvious thatσw/Um has higher values in the core region in the downstream measuring section, but lower in the sound flow region (Fig.8a).
Therefore, the turbulence level increases downstream in the vortex core, and decreases in the main flow region.
The characteristics of the curves Sw are various, but in principle the values are increased downstream, i.e., nega- tive values become more negative and positive even more positive (Fig.8b). They differ from the values for normal, Gaussian distribution. The values Fw have in the great- est part of the section z/D = 26.31 higher values than
those in z/D= 3.35, which is important for the domain of vortex core and shear layer. These distributions point out the intermittent character of the generated turbulent swirl flow, as well as the existence of the organized coher- ent structure in the vortex core and shear layer.
4.1.3 Autocorrelation function
The correlation theory incorporates important state- ments about the structure and statistical nature of
(a) (b)
Fig. 9. Coefficients of time autocorrelation functions for circumferential fluctuating velocity Rww (τ) in measuring section z/D= 3.35, planeϕ= 270◦, regimen= 1500 rpm, for times: (a) τ [s] = 0.1 and (b) 0.02.
turbulence. Here, due to the research topic – swirl, it is measured and analyzed the normalized time autocor- relation function for circumferential fluctuating velocity defined as follows:
Rww(τ) =w(t)w(t+τ)/σ2w (3) which is referred to as the coefficient of time autocorrela- tion function, or the time autocorrelation coefficient. Dis- tributions of autocorrelation coefficientRww (τ) are pre- sented on the basis of measurements in the sectionz/D= 3.35, plane ϕ = 270◦, for the regime n = 1500 rpm, in points which belong to the characteristic flow regions.
Correlation curves are presented for two maximum timesτ, to better focus on the existent differences in cor- relation dependencesw(t)w(t+τ) in the regions of vor- tex core, shear layer and main flow. Namely, the forms of experimentally determined correlation curves indicate various dynamics of fluctuating circumferential veloc- ity fields in measuring points. Sets of correlation curves Rww (τ) change the sign several times, asymptotically approaching the zero value (Fig. 9). Correlation curves change their positions, depending on the section zone and correlation time τ. In points r/R = 0.58 and 0.68 there are changes of correlation coefficients significance, i.e., extremely great withτ increase. It means that high frequency components of circumferential fluctuating ve- locities play the main role in this region. The character of correlation curves in the core (r/R= 0.04; 0.09 and 0.19) and shear layer (0.18< r/R <0.38) shows the dominant role of low frequency fluctuations (Fig.9).
Negative values of the correlation function indicate the presence of periodical behaving in the fluctuating circum- ferential velocity field, when low frequency fluctuations are dominating. In this sense, timeτ0, which denotes time
interval till the firstRww(τ0) = 0, is related to the dom- inant frequency of circumferential velocity fluctuations, when the spectral density maximum occurs. Timeτ0can be related to the average frequency of fluctuating circum- ferential velocities, however, certain analytical relations of these parameters exist only in a strongly expressed periodicity.
4.2 Stereo PIV measurements 4.2.1 Velocity distributions
Stereo PIV measurements in specified cross-sections provided the distributions of averaged velocity magni- tude (c= (U2+V2+W2)0.5) on the basis of 400 images (Fig.10).
Quality measurement area in the measuring section z/D= 3.35 has maximum dimensions of app. 180 mm× 100 mm, while in the second measuring section 200 mm× 100 mm. In this way, most of the measuring section is cap- tured in the second case in thex-axis directionr/R≈0.5.
The Rankine vortex structure of the turbulent swirl flow is generated by the axial fan and part of it is measured with stereo PIV. In this way, the vortex core and shear layer regions are captured, while in some directions the sound flow region as well. The wall region is not intended to be captured in these measurements.
The maximum velocity achieved in the measuring cross-sectionz/D= 3.35 iscmax,1≈18.4 m.s−1, while in the second measuring section it is approximatelycmax,2≈ 15 m.s−1. In both cases it is achieved in the outer regions.
Velocity decrease is in correlation with the fact that tur- bulent swirl flow decays downstream and that velocity field redistribution occurs. The vortex center, defined as
(a) (b)
Fig. 10. Average velocity magnitude distributions in measuring cross-sections for regimen= 1500 rpm: (a) z/D= 3.35 and (b)z/D= 26.31.
(a) (b)
Fig. 11.Average velocity magnitude distributions in vertical meridian sections for regime n= 1500 rpm: (a)z/D= 3.35 and (b)z/D= 26.31.
the velocity magnitude minimum, is not on the pipe axis, nor is it in both cases in the third quadrant. Performed LDA measurements have also shown asymmetrical swirl behavior.
Averaged velocity magnitude of 400 pictures, obtained by stereo PIV measurements with the sampling rate of 2 Hz in both measuring vertical meridian sections, is presented in Figure 11. Captured area in the section z/D= 3.35 is app. 135 mm×80 mm, while in the sec- ond section app. 145 mm × 85 mm. In this way, only r/R ≈ 0.36 is reached, while flow downstream develop- ment can be observed. The results of the measurements in the adequate cross- and vertical meridian sections are in correspondence. The Rankine vortex structure is also detected in this plane (Fig.11).
This correspondence is obvious in the velocity inten- sity and distribution, as well as in the velocity magnitude minimum positions. The velocity magnitude minimum is about 5 mm under the pipe axis in the first section (Fig. 11a), while it is higher in the second (Fig. 11b).
These measurements were performed in completely differ- ent times, what proves the assumption about the quasi- stationary flow.
Figure 12 shows the average velocity magnitude dis- tribution in the measuring section z/D= 3.35, sampled with 7 Hz and averaged on the basis of only 99 pictures, due to the limitations in RAM. It is obvious that results correspond to those sampled with 2 Hz in the same mea- suring section. This again proves the assumption about the quasi-stationary flow.
Distribution of the averaged velocity magnitude pre- served a similar character, while magnitudes are slightly different. Distributions of the average axial and circumfer- ential velocities on the basis of 400 pictures in the vertical meridian section with origin inz/D= 3.35 are presented in Figure13.
The Rankine vortex structure of the turbulent swirl flow is obvious in the captured regions: vortex core, shear layer and only a part of the sound flow region. Both veloc- ities are symmetrically distributed. However, the vortex
Fig. 12.Average velocity magnitude (c) in the vertical meridian section in origin z/D= 3/35 obtained with 7 Hz for regime n= 1500 rpm.
(a) (b)
Fig. 13.Average velocities in the vertical meridian section with origin inz/D= 3.35 and for regimen= 1500 rpm: (a) axial (U) and (b) circumferential (W).
core center and pipe axis do not overlap, as reported above. Reverse flow is obvious in the vortex core center for the axial velocity in Figure13a. Circumferential veloc- ity has linear distribution in the vortex core region, which is a characteristic of solid body structure. It reaches its maximum intensities, like axial velocity and velocity mag- nitude, in the outer regions. Negative values of circumfer- ential velocity originate from the software nomenclature.
All these experimental results and analyses reveal the turbulent swirl flow field, generated behind the axial fan without the guide vanes, durability and complexity. Addi- tional hydraulic elements, such as valves, elbows, diffusers and etc., which is a case in the ventilation systems, can only generate more complex cases and even increase hy- draulic losses and power consumption [5]. This implies
that turbulent swirl flow should always be considered in designing ventilation systems.
4.2.2 PIV measuring uncertainty
The sources of systematic error in the case of the stereo PIV measurements are calibration and data acqui- sition. Detailed analyses of all errors for the stereo PIV system used in these experiments are presented in ref- erence [17]. For the fan rotation speeds n = 1000, 1500 and 2000 rpm, the laser interval between the pulses was Δt = 60, 40 and 30 μs, respectively. “Frozen” particles are omitted in this way. The velocity measuring uncer- tainty by the use of stereo PIV considering measurement uncertainty of space and time is defined in reference [18].
(a) (b)
Fig. 14.Measuring sectionz/D= 3.35 and rotation numbern= 1500 rpm: (a) positions of the velocity magnitude minimum and (b) histogram of the number of repetitions of the positions of the velocity magnitude minimum in the (x,y) plane.
It seems that the biggest error source is particle move (Δx). The rule of five particle pairs inside each interroga- tion area, omitting pixel blockage, excellent camera focus on particles andΔtcheck aid in decreasing of this error.
Used algorithms for data processing are reported in the Section 3.2. Percentage of the interpolated vectors is not higher than 5%. Both cameras result with a small parti- cle move in the vortex region, which is lower than 0.5 pix and higher, app. 4 pix, for other flow regions. Anyhow, it is shown [5] that in this way the error is 1.25% in the region of shear layer and sound flow region, while it is almost ten times higher in the vortex core region. So, it is almost impossible to measure the whole turbulent swirl flow region at once with equally distributed error.
4.2.3 Investigation of vortex core dynamics
Analyses of turbulent velocity field and its structural parameters have shown that characteristic asymmetry of the distribution of measured statistical parameters exists.
The vortex core dynamics is directly related to these ef- fects. The principle of the velocity magnitude minimum has been involved as the criterion for vortex core dynam- ics study. Namely, a set of statistical points with a com- mon property is determined on the basis of measurement results. The common property is the velocity magnitude minimum for at least once. Further statistical-numerical procedure calculates repeatability of the velocity magni- tude minimum in the point which is a member of this set of points. Data sampling rate is 2 Hz for 400 images, i.e., realizations, while 7 Hz gave 99 images. Positions of the velocity magnitude minima for 400 images acquired with 2 Hz in the measuring section, are presented in Figure14a.
The geometry center of all 400 positions is marked with a small cross, while the minimum of the average velocity field is marked with a big black cross. They al- most totally overlap and both markers are in the third quadrant. However, all 400 points are not visible, be- cause a great percentage of them is repeated. Only 11.5%
in z/D = 3.35, while 36% in the measuring section z/D = 26.31, are unique. It is clear that the number of unique points is significantly bigger in the downstream section, and therefore the vortex core dynamics is greater in this section. Figure 15b shows a histogram with the number of repetitions in the cross-section z/D = 3.35, also for data sampling rate of 2 Hz. The histogram pro- vides a number of repetitions of the velocity magnitude, i.e., vortex core center, in each point of the measuring section.
The histogram (Fig.14b) can also reveal isolines (lines with the same number of repetitions of the position of the velocity magnitude minimum presented in Fig. 15a).
Comparison with the isolines in Figure15b for the same flow regime (n= 1500 rpm), but in the measuring section z/D = 26.31, leads to the conclusion that a more nar- row area of the precession movement of the vortex core is downstream. It is obvious that in section z/D = 3.35 there exist the positions with double the number of max- imum repetitions in sectionz/D= 26.31.
It is interesting to show that the character remains almost the same and even for higher data sampling rate, but only 99 images (Fig.16).
The region of turbulent vortex core movement is de- fined in this way. These developed and applied meth- ods are significant for further statistical investigations of the vortex structure and intermittency of vortex coherent
(a) (b)
Fig. 15.Isolines of the repetition number of the velocity magnitude minimum positions for the regimen= 1500 rpm and data sampling rate 2 Hz in sections: (a)z/D= 3.35 and (b)z/D= 26.31.
(a) (b)
Fig. 16.Isolines of the repetition number of the velocity magnitude minimum positions for the regimen= 1500 rpm and data sampling rate 7 Hz in sections: (a)z/D= 3.35 and (b)z/D= 26.31.
structures in the core and shear layer of the investigated turbulent swirl flow behind the axial fan impeller.
5 Conclusions
Specially designed axial fan impeller was used with- out guide vanes to generate the turbulent swirl flow in the pipe. One-component LDA and stereo PIV measur- ing techniques were employed in this study. Characteris- tic regions: vortex core, shear layer and almost the whole
sound flow region were measured. LDA measurements re- vealed flow integral parameters and turbulence statistics.
Non-dimensional velocity profiles show various behaviors.
It is shown that obtained axial velocity profiles in measur- ing sectionz/D = 3.35 are similar for various Reynolds numbers. Axial velocity was not transformed downstream almost at all, while circumferential changed the intensity, but not the character. Average circulation in the mea- suring section is decreased downstream. In both measur- ing sections radial velocity has the highest values in the vortex core region.
body structure. It is also shown that the average veloc- ity magnitude profile in the downstream section is trans- formed, but the character of the Rankine vortex remains.
Despite the existing vortex core dynamics, the assump- tion about the quasi-stationary flow is proved by com- paring the velocity intensities and distributions in cross- and vertical meridian sections, and by applying lower and higher data sampling rates.
Investigation has revealed and proved turbulent swirl flow endurance. This should be considered in designing energy efficient ventilation systems and choosing fans, which are still in most cases built in without guide vanes.
Acknowledgements. Axial fan is designed by Prof. Dr.-Ing.
Zoran Proti´c† (1922–2010) and Prof. Dr. Zoran Stojiljkoviæ designed and built a very precise original fan rotation speed regulator. This research was financially supported by the Min- istry of Education, Science and Technological Development, Republic of Serbia, Project No. TR 35046, what is gratefully acknowledged.
References
[1] K. Yokota, K. Kurahara, D. Kataoka, Y. Tsujimoto, A.J.
Acosta, A study of swirling backflow and vortex structure at the inlet of an inducer, JSME Int. J. Ser. B 42 (1999) 451–459
[2] F. Bario, T.M. Faure, E. Jondeau, J.-L. Normand, J.-M.
Nguyen Duc, Analysis of inducer recirculating inlet flow, J. Propul. Power 19 (2003) 52–528
[3] W.T.W. Cory, Fans and ventilation: A practical guide, Roles & Associates Ltd, Elsevier, 2005
[4] M.H. Beniˇsek, S.M. Cantrak,ˇ M.S. Nedeljkovi´c, Theoretical and experimental investigation of the turbulent swirling flow characteristics in circular pipes, ZAMM 68 (1988) 280–282
[5] D.S. ˇCantrak, Analysis of the vortex core and turbu- lence structure behind axial fans in a straight pipe us- ing PIV, LDA and HWA methods, Ph. D. thesis (in Serbian), University of Belgrade, Faculty of Mechanical Engineering, Belgrade, 2012
M. Gabi, Investigations on the swirl flow caused by an ax- ial fan: A contribution to the revision of ISO 5801, in: Fan 2012, International Conference on Fan Noise, Technology and Numerical Methods, Senlis, France, 2012
[9] J.M.F. Oro, R. Ballesteros-Tajadura, E.B. Marigorta, K.M.A. D´ıaz, C.S. Morros, Turbulence and secondary flows in an axial flow fan with variable pitch blades, J.
Fluids Eng. 130 (2008) 041101.1–041101.11
[10] Z.D. Proti´c, M.S. Nedeljkovi´c, D.S. Cantrak, N.Z.ˇ Jankovi´c, Novel methods for axial fan impeller geometry analysis and experimental investigations of the generated swirl turbulent flow, Thermal Sci. 14 (2010) 125–139 [11] J. Guangyuan, H. Ouayang, D. Zhaohui, Experimental
investigation of unsteady flow in axial skewed fans ac- cording to flow rates, Exp. Thermal Fluid Sci. 40 (2013) 81–96
[12] W. Steenbergen, J. Voskamp, The rate of decay of swirl in turbulent pipe flow, Flow Meas. Instrum. 9 (1998) 67–78 [13] J.M. Burazer, M.R. Leˇci´c, S.M. ˇCantrak, On the non- local turbulent transport and non-gradient thermal diffu- sion phenomena in HVAC systems, FME Trans. 40 (2012) 119–125
[14] S.S. Risti´c, J.T. Ili´c, D.S. ˇCantrak, O.R. Risti´c, N.Z.
Jankovi´c, Estimation of laser-Doppler anemometry mea- suring volume displacement in cylindrical pipe flow, Thermal Sci. 16 (2012) 1127–1142
[15] J.T. Ili´c, S.S. Risti´c, D.S. ˇCantrak, N.Z. Jankovi´c, M.
Sre´ckovi´c, The comparison of air flow LDA measurement in simple cylindrical and cylindrical tube with flat exter- nal wall, FME Trans. 41 (2013) 333–341
[16] S. Wereley, L. Gui, A correlation-based central differ- ence image correction (CDIC) method and application in a four-roll mill flow PIV measurement, Exp. Fluids 34 (2003) 42–51
[17] J.G. Leishman, M. Ramasamy, Benchmarking PIV with LDV for rotor wake vortex flows, Collection of Technical Papers – AIAA Appl. Aerodyn. Conf. 3 (2006) 1796–1824 [18] R.J. Adrian, Particle-imaging techniques for experimen- tal fluid mechanics, Annu. Rev. Fluid Mech. 23 (1991) 261–304
